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May 20th

May 20th

# MATH 116 EXAM

6 points

1. For the quadratic function f (x) = x2-3x-28, find

a) the x- intercepts , and

b) the y-intercept.

x-intercepts: (-4,0) and (7,0)
y-intercept: (0,-28)

7 points

2. Identify the equations .html">vertex of the quadratic function f (x) = 7x2-28x+58.

Vertex: (2,30)

7 points

7 points

4. De termine if x -5 is a factor of f (x) = x3 -8x2 -55x+350. If x-5 is a factor of the polynomial then factor
the polynomial completely.

Is x-5 a factor? Yes

If so the factorization is x3+4x2-31x-70 = (x-5) (x-10)(x+7)

7 points

5. Factor the polynomial f (x) = 6x2+19x-7 completely

7 points

6. Factor the polynomial f (x) = x2-13x+36 completely.

7 points

7. Find a polynomial with real coefficients that has the zeros 6 and 3+i.

6 points

8. List all possible rational zeros of f (x) = 14x3-65x2-26x+5 using the rational zero test .

7 points

9. Find all real zeros of the function f (x) = x9-24x8+144x7. Give the multiplicity of each repeated zero.

x = 0 is a zero of multiplicity 7
x = 12 is a zero of multiplicity 2

6 points

10. Use the Leading Coefficient Test to determine the extreme right-hand and left-hand behavior for the graph of
f
(x) = -4x7+63x4-3x2+1. Demonstrate this behavior with a picture.

7 points

11. Find the domain of the rational function Give the answer in interval notation.

7 points

12. For the rational function find

a) the x-intercepts, and

b) the y-intercept.

6 points

13. Find any vertical asymptotes of the rational function

6 points

14. Find the horizontal asymptote of the rational function

7 points

15. Find the oblique asymptote of the rational function

Formulas

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